Current Global Navigation Satellite Systems (GNSS), such as Global Positioning Systems (GPS), must compensate for multiple error sources. One challenging technical issue that exists in Real-Time Kinematic (RTK) GNSS navigation is integer ambiguity resolution. Once the integer vector is resolved, centimeter-level positioning estimation accuracy can be achieved using the GNSS carrier-phase measurements. Recently, a real-time, sliding window, Bayesian estimation approach to RTK GNSS and inertial navigation was proposed to provide reliable centimeter-accurate state estimation, via integer ambiguity resolution utilizing a prior along with all Inertial Measurement Unit (IMU) and GNSS measurements within the time window. One challenge to implementing that approach in practice is the high computational cost.
Integration of GNSS and aided inertial navigation systems (INS) has proven useful due to their complementary natures. The INS provides a continuous, high-bandwidth state vector estimate. GNSS aiding corrects errors accumulated by the integrative INS process and calibrates the IMU. The overall accuracy of GNSS-aided INS depends on the accuracy, frequency, and reliability of the GNSS measurements. For example, a well-designed GPS receiver typically can reach stand-alone positioning accuracy of 3 m to 8 m. To achieve higher accuracy positioning reliably, differential GPS (DGPS) is used. With a base station within a range of a few tens of kilometers, DGPS accuracy is on the order of 1 m, growing at the rate of 1 m per 150 km of separation. A user can either set up a base station on their own or use data from a publicly available correction service, such as Continuously Operating Reference Station (CORS), Nationwide Differential Global Positioning System (NDGPS), and the Regional Reference Frame Sub-Commission for Europe (EUREF). As mobile communication networks (e.g., 4G or WiFi) become readily available, DGPS techniques will become ubiquitous.
GNSS receivers provide carrier-phase measurements that are biased by an unknown integer number of wavelengths. While the Phase-Lock-Loop (PLL) of a receiver channel maintains phase lock, the unknown integer for the satellite being tracked remains constant. When loss-of-lock eventually happens (e.g., a cycle-slip occurs), the new integer is likely to be different. The fundamental ideas underlying integer ambiguity resolution rely on reformulating the problem into an Integer Least Square (ILS) approach, e.g. Least-squares AMBiguity Decorrelation Adjustment (LAMBA), modified LAMBDA (MLAMBDA), or Mixed IntegerLEast Squares (MILES). RTK applications solve the ILS and position estimation problems simultaneously in real-time. Solution of the RTK problem is simplified, yet still challenging, when dual-frequency receivers are available, because the integers can be resolved by forming wide-lane phase measurements. When the integer vector can be resolved, centimeter positioning-accuracy is achievable in real-time on moving platforms. The performance of the conventional single-epoch resolution is strongly influenced by the number of available satellites, the geometry of the received satellite constellation, and the quality of the measurements. If noisy or faulty measurements exist, the integer resolution can be wrong, without sufficient measurement redundancy to detect the error. For single-frequency receivers, integer ambiguity resolution is even more challenging due to the inability to form the wide-lane measurement and the smaller number (e.g., half) of measurements.
Measurement redundancy enhances the ability to identify the correct integers at the expense of additional computation. For either single or dual frequency receivers, redundancy can be enhanced by accumulating GNSS measurements over a multi-epoch window. The redundancy is further enhanced when an inertial measurement unit (IMU) is available to provide kinematic constraints between the state vectors at the epoch measurement times. What is needed for real-time applications is a computationally-efficient solution for integer ambiguity resolution combining GNSS, IMU, and prior knowledge of state information (e.g., a priori state information).
In the following detailed description of systems and methods for carrier-phase integer resolution, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments in which the inventive subject matter may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice them, and it is to be understood that other embodiments may be used and that structural, logical, electrical, and other changes may be made without departing from the scope of the inventive subject matter. Such embodiments of the inventive subject matter may be referred to, individually and/or collectively, herein by the term “invention” or “subject matter” merely for convenience and without intending to limit the scope of this application voluntarily to any single invention or inventive concept if more than one is in fact disclosed. The following description is, therefore, not to be taken in a limited sense, and the scope of the inventive subject matter is defined by the appended claims.